You are given a string $s$ consisting of $n$ lowercase Latin letters. $n$ is even.
For each position $i$ ($1 \le i \le n$) in string $s$ you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters '_a_' and '_z_' have only one of these options). Letter in every position must be changed **exactly once**.
For example, letter '_p_' should be changed either to '_o_' or to '_q_', letter '_a_' should be changed to '_b_' and letter '_z_' should be changed to '_y_'.
That way string "_codeforces_", for example, can be changed to "_dpedepqbft_" ('_c_' $\rightarrow$ '_d_', '_o_' $\rightarrow$ '_p_', '_d_' $\rightarrow$ '_e_', '_e_' $\rightarrow$ '_d_', '_f_' $\rightarrow$ '_e_', '_o_' $\rightarrow$ '_p_', '_r_' $\rightarrow$ '_q_', '_c_' $\rightarrow$ '_b_', '_e_' $\rightarrow$ '_f_', '_s_' $\rightarrow$ '_t_').
String $s$ is called a palindrome if it reads the same from left to right and from right to left. For example, strings "_abba_" and "_zz_" are palindromes and strings "_abca_" and "_zy_" are not.
Your goal is to check if it's possible to make string $s$ a palindrome by applying the aforementioned changes to every position. Print "_YES_" if string $s$ can be transformed to a palindrome and "_NO_" otherwise.
Each testcase contains several strings, for each of them you are required to solve the problem separately.
## Input
The first line contains a single integer $T$ ($1 \le T \le 50$) — the number of strings in a testcase.
Then $2T$ lines follow — lines $(2i - 1)$ and $2i$ of them describe the $i$\-th string. The first line of the pair contains a single integer $n$ ($2 \le n \le 100$, $n$ is even) — the length of the corresponding string. The second line of the pair contains a string $s$, consisting of $n$ lowercase Latin letters.
## Output
Print $T$ lines. The $i$\-th line should contain the answer to the $i$\-th string of the input. Print "_YES_" if it's possible to make the $i$\-th string a palindrome by applying the aforementioned changes to every position. Print "_NO_" otherwise.
[samples]
## Note
The first string of the example can be changed to "_bcbbcb_", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters.
The second string can be changed to "_be_", "_bg_", "_de_", "_dg_", but none of these resulting strings are palindromes.
The third string can be changed to "_beeb_" which is a palindrome.
The fifth string can be changed to "_lk_", "_lm_", "_nk_", "_nm_", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "_ll_" or "_mm_".
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ n_k \in \mathbb{Z} $ be the length of string $ s_k $, with $ n_k $ even and $ 2 \leq n_k \leq 100 $.
- Let $ s_k = (s_{k,1}, s_{k,2}, \dots, s_{k,n_k}) $ be a string of $ n_k $ lowercase Latin letters.
For each character $ s_{k,i} $, define its possible transformations:
- If $ s_{k,i} = \texttt{'a'} $, then $ \text{next}(s_{k,i}) = \{\texttt{'b'}\} $.
- If $ s_{k,i} = \texttt{'z'} $, then $ \text{next}(s_{k,i}) = \{\texttt{'y'}\} $.
- Otherwise, $ \text{next}(s_{k,i}) = \{ \text{prev}(s_{k,i}), \text{next}(s_{k,i}) \} $, where:
- $ \text{prev}(c) $ is the preceding letter in the alphabet,
- $ \text{next}(c) $ is the succeeding letter in the alphabet.
Let $ S_k = (s_{k,1}', s_{k,2}', \dots, s_{k,n_k}') $ be a transformed string such that $ s_{k,i}' \in \text{next}(s_{k,i}) $ for all $ i \in \{1, \dots, n_k\} $.
**Constraints**
1. $ 1 \leq T \leq 50 $
2. For each $ k \in \{1, \dots, T\} $:
- $ n_k $ is even, $ 2 \leq n_k \leq 100 $
- $ s_{k,i} \in \{\texttt{a}, \dots, \texttt{z}\} $ for all $ i \in \{1, \dots, n_k\} $
- Each character is changed *exactly once* to one of its valid neighbors (no stay).
**Objective**
Determine whether there exists a transformed string $ S_k $ such that $ S_k $ is a palindrome, i.e.,
$$
s_{k,i}' = s_{k,n_k+1-i}' \quad \text{for all } i \in \{1, \dots, n_k/2\}.
$$
Output "YES" if such $ S_k $ exists; otherwise, output "NO".